Phase Cycling In Inept

All NMR experiments are beset by artifacts: peaks in the spectrum that are not supposed to be there. They may be caused by imperfectly calibrated pulses, by delays (such as 1/(2./)), that cannot be set perfectly for every resonance in the spectrum, or by hardware imperfections. We can also speak of coherence pathways—different origins and histories of NMR magnetization that eventually reach the receiver during the FID. We saw in the previous section, for example, that observable 13 C coherence can come from 1H "polarization" (population difference) via INEPT transfer, or it can come from 13 C polarization directly as a result of the final 13 C 90° pulse. These two components result in the antiphase (+4, -4) 13C spectrum and the in-phase (+1, + 1) 13C spectrum combined in the receiver. If we view the direct (13C i 13C) pathway as an artifact, we can explore methods to remove it. There are two main techniques for removing artifacts: pulsed field gradients (which we will discuss in Chapter 8) and phase cycling. Phase cycling is a subtraction method, which relies on acquiring more than one scan and combining the FIDs (by adding or subtracting) in such a way that the desired signals add together and the artifacts cancel out by subtraction. A phase cycle for INEPT can be designed very easily by looking at the product operator description at each stage of the experiment. By changing the phase of one of the pulses, we can differentiate between the desired operators (the "signal") and the undesired operators (the "artifacts"). Starting from the equilibrium state, we have

1Hand13C90° pulses on -

Note that the conversion S2 i Sx in the last step is brought about by the 90° 13C pulse only; the 90° 1H pulse has no effect on this conversion. The desired term, 4[-2SxIz ], comes from 2IxSz and requires both 90° pulses, on 1H and 13C, to be produced. Consider what happens if we change the phase of the 1H 90° pulse from +/ to -/:

By inverting the phase of the 1H 90° pulse (+/ to -/), we have inverted the phase of the resulting antiphase 13 C signal. If we choose the +X axis as our phase reference, the -2SxIz term will give an antiphase doublet with the downfield (left) component negative (upside-down) and the upfield (right) component positive (Fig. 7.25, top left). The 2SxIz term will give the opposite spectrum: downfield component positive and upfield component negative (Fig. 7.25, top center). The final Sx term will be positive and in-phase in

either case:

1H90o on+y and 13C90o on+y Sz ^ Sx

Only the 13 C 90o pulse operates on Sz to rotate it to Sx, so the phase of the 1H 90o pulse is irrelevant (Fig. 7.25, bottom left and bottom center). Now we can apply the phase-cycling strategy: acquire one FID using the 1H 90o pulse on +/ and a second FID with the 1H 90o pulse on — /. Subtract the second FID from the first. The result will be:

Difference = {4[—2SX Iz ] + Sx} — |4[2SX Iz ] + Sx} = 8[—2SX Iz ]

Fourier transformation will give a spectrum corresponding to 8[—2Sx Iz ]: an antiphase 13 C doublet with intensities of —8 (1H = a component) and +8 (1H = 5 component) (Fig. 7.25, right). This spectrum is the pure INEPT spectrum, without any contribution from the in-phase 13C doublet (the "artifact"). If you understand this strategy of cancellation, you will understand the use of phase cycling in all NMR experiments: pick a pulse whose phase has a different effect on the desired signal than on the artifact peaks, change its phase over more than one scan, and combine the FIDs by addition or subtraction so as to cancel the artifact signals and sum the desired signals.

Figure 7.26 (left) shows the INEPT spectrum of neat benzene (C6H6) using the sequence of Figure 7.16 with no 1H decoupling and no phase cycling. With the final 1H pulse phase set to 1 (/ axis), we see the H = a component upside-down with intensity 3 and the H = 5 component positive with intensity 5 (spectrum A). With the final 1H pulse phase set to 3 (— / axis), the antiphase (—4, +4) portion of the signal is inverted (spectrum B), giving intensities of +5 (H = a) and — 3 (H = ¡). If the FIDs from spectrum A and spectrum B are subtracted, Fourier transformation of the difference FID gives only the portion of the signal that results from coherence transfer from 1H to 13 C: an antiphase doublet with intensities of — 8 (H = a) and +8 (H = ¡). If instead the two FIDs are added together, Fourier transformation of the sum FID gives only that portion of the signal that results from direct excitation of the 13C z magnetization: an in-phase doublet with intensities of

Figure 7.26

+2 (H = a) and +2 (H = ft). Note that the intensities add directly from the two scans, but the noise increases as the square root of the number of scans increases, so the noise in the sum and difference spectra (right) is V2 times larger (1.414 times larger) than in the individual scan spectra (left).

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